Question

In: Statistics and Probability

1. Out of a sample of 100 purchase orders, 10 contain errors. What is the confidence...

1. Out of a sample of 100 purchase orders, 10 contain errors. What is the confidence interval for 95% confidence?

2. For a 95% confidence level, what is the value n (sample size) when π = .15 and the sampling error is .07?

a.99.96

b.61.47

c. 96.04

d.51.00

Solutions

Expert Solution

CI=( 0.041, 0.159)
99.96 (option a)

Explanation:

CONFIDENCE INTERVAL FOR A POPULATION PROPORTION.

n=100

x=10(Sample size, Number of trials).(Number of success).

1−α=0.95(Confidence level).

Choice of statistic

Confidence interval for a population proportion.

If p^ is the proportion of observations in a random sample of size n that belongs to a class of interest, a 100 (1−α)%confidence interval on the proportion p of the population that belongs to this class is:

Sample proportion.

Calculus of zα/2− value.

1−α=0.95

α=1−0.95

α=0.05

α/2=0.05/2

α/2=0.0250
Calculus of zα/2 using the cumulative standard normal distribution table.

We search through the probabilities to find the value that corresponds to 0.9750.

we find 0.9750 exactly, therefore

zα/2 =1.9+0.06=1.96

Calculus of the confidence interval using the direct method.

(2)

1−α=0.95 (Confidence level)

E=0.07 (Error)

p^=0.15..(Initial estimate of p)

Sample size.

Calculus of zα/2− value.

1−α=0.95

α=1−0.95

α=0.05

α/2=0.05/2

α/2=0.0250

Calculus of zα/2 using the cumulative standard normal distribution table.

We search through the probabilities to find the value that corresponds to 0.9750.

orchestra answered 1 year ago

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